Sunday, October 12, 2008

A Freeway Congestion Pricing Paradox

Patrick DeCorla-Souza, an expert on congestion pricing with the Federal Highway Administration (FHWA), explains how congestion pricing can actually increase the volume of traffic during peak periods as well as reduce congestion.

(with apologies to Chao Chen and Pravin Varaiya, who wrote an article with a similar title “The Freeway Congestion Paradox� in 2002)

A primary goal of congestion pricing of entire roadways (all lanes) is to reduce vehicle use during peak hours in order to reduce congestion. Congestion pricing of roadways into the central areas of London, Stockholm and Singapore has demonstrated the ability of pricing to reduce excessive traffic and thereby alleviate congestion.

Therefore, it is not difficult for transportation professionals to accept that congestion pricing of a freeway (all lanes) could have a similar effect – reducing both traffic volumes and congestion during peak hours. However, this discussion attempts to explain a seeming paradox – that congestion pricing, if well designed and combined with active traffic management, could actually increase traffic volumes served on a freeway during peak periods (in addition to person throughput).

Let’s consider a freeway with the following vehicular demand (i.e., vehicles arriving) at a bottleneck location during the morning peak period, expressed as vehicles per lane (vpl):

5am to 6 am 1400
6 am to 7 am 2200
7am to 8am 2400
8am to 9 am 2200 (plus 400 queued)
9 am to 10am 1400 (plus 600 queued)
Total 9600

With a low demand of 1400 vehicles per lane per hour, traffic flows freely from 5 to 6am, exceeding 60 mph. In the next hour, demand reaches the sustainable capacity of 2200 vehicles per lane per hour (based on TRB’s Highway Capacity Manual), and traffic flows more slowly averaging 45 to 50 mph. Demand reaches 2400 vehicles per lane over the next hour (7 to 8 am) causing the flow of traffic to break down and speeds to be erratic. With this breakdown in flow, throughput through the bottleneck drops to 2000 vehicles per lane per hour. (This is consistent with the approximately 10 percent drop in throughput observed at bottleneck locations when flow breaks down). Consequently a queue of 400 vehicles per lane (vpl) is formed at the bottleneck by the end of this hour. Demand during the next hour (8 to 9 am) drops to 2200 vehicles per lane. But since traffic flow is now in the breakdown condition, throughput is still 2000 vehicles per lane per hour. Therefore, at the end of this hour, the queue length increases from 400 vpl to 600 vpl. In the final hour of the morning peak period (9 to 10 am), demand drops to 1400 vpl. Thus, by the end of this hour, the 600 vpl queue is cleared, at the lowered throughput rate of 2000 vpl.

Now let us consider the same bottleneck with a well-designed congestion pricing strategy designed to maximize vehicle throughput by combining it with active traffic management, including ramp metering. Active traffic management and pricing complement one another, for the following reasons:
· Demand varies significantly from day to day for a variety of reasons. However, on a priced freeway, prices must be pre-scheduled (rather than set dynamically) since the entire freeway is being priced. Drivers will need to know the toll rates before they leave their origins, rather than on the trip, since they will not have a choice once they are on the freeway. Therefore, if pricing is deployed by itself, prices would have to be set high enough to keep demand much below the sustainable capacity level. If pricing is deployed with active traffic management, however, ramp metering could be used to hold excess demand at on-ramps if and when this may cause traffic flow to break down, and speed harmonization could be used to delay the breakdown of traffic flow.
· Ramp metering by itself has limited applicability for severely congested freeway systems, because queues at on-ramps can get too long and disrupt traffic flow on the surface street system. But since pricing encourages some drivers to travel at other times, on other modes or on other routes, the total number of vehicles queuing at on-ramps would be reduced, making it easier to deploy ramp metering effectively. (Note: Fairness issues relating to longer queues at ramp meters in inner cities are easily addressed – toll credits may be provided based on the amount of time spent in the queue).
· Speed harmonization, by itself, is capable of delaying the breakdown of traffic flow. But when combined with pricing, excessive demand can be curbed, thus potentially allowing speed harmonization to keep traffic flowing throughout the peak period.

Thus, active traffic management must be a key part of the overall freeway congestion pricing strategy, in order to prevent the breakdown of traffic flow and maximize vehicle throughput. Revenues from pricing may be used to pay for investment in active traffic management infrastructure and operations. Gantries used for lane control and speed harmonization may also be used to mount electronic toll readers and enforcement cameras. As a metropolitan area grows and travel demand increases, toll rates will increase to balance demand and supply, providing the extra revenue needed for additional investment in highway or transit capacity through the bottleneck. The overall strategy will create a “FAST� system that will be:
· Flexible enough to respond to varying levels of demand throughout the peak period
· Actively-managed to prevent breakdown of traffic flow and maximize safety
· Sustainable financially through the longer term future as a metro area grows
· Throughput-maximizing

Now let’s consider the same freeway discussed above, with the “FAST� approach. With graduated variable tolls between 6am and 9am, the FAST approach can keep traffic at the level of sustainable capacity, and may result in the following shifts in vehicular demand (i.e., arrivals) at a bottleneck location during the morning peak period, expressed as vehicles per lane (vpl):

5am to 6 am 1500 (increased by 100)
6 am to 7 am 2200 (same)
7am to 8am 2200 (reduced by 200)
8am to 9 am 2200 (same)
9 am to 10am 1500 (increased by 100)
Total 9600

In reality, some vehicles may shift to alternative toll-free routes to avoid the toll, while others who previously used the alternative toll-free routes may shift to the freeway to take advantage of the travel time savings and reliability of service. Traffic may increase by 100 vpl from 5 to 6am, since some travelers may shift to avoid the tolls beginning at 6am. In the next hour, demand is kept at the sustainable capacity of 2200 vehicles per lane per hour, because the 100 vpl demand that shifts to the earlier hour is replaced by 100 vpl shifting from the 7 to 8 am hour to get a lower toll rate. Demand is reduced to the sustainable capacity of 2200 vehicles per lane over the next hour (7 to 8 am) because 100 vpl shift to the earlier 6 to 7 am hour and another 100 vpl shift to the later 8 to 9am hour to get a lower toll rate. Demand during the next hour (8 to 9 am) stays at 2200 vehicles per lane (the sustainable capacity), because the 100 vpl that shift from the earlier hour to this hour are balanced by 100 vpl that shift from this hour to the 9 to 10am hour to avoid paying tolls. Consequently, the total demand in the 9 to 10am hour increases to 1500 vpl.

The reader will note that total vehicle “throughput� as presented above for the 5-hour morning peak period is 9600 vpl for each case. This assumes that there will be no mode shifts and no route shifts. I acknowledge that these are not realistic assumptions. Depending on the nature of the corridor and available transit and ridesharing options, one could expect a further reduction in vehicular demand of 100 to 1000 vpl over the 5- hour period, which would be replaced by “new� vehicles that are either diverted from some other route or time of travel, or are completely new “induced� trips. Person throughput in the corridor may thus be expected to increase.

The big question is – what will happen in the 9 to 10 am hour, during which travel is toll-free and which carries only 1500 vpl vs. 2000 vpl in the base case without pricing. Will the spare capacity, available toll-free, result in new trips or from trips being diverted from some other route or time of travel? Since the 9 to 10 am hour was congested and in breakdown flow condition in the base case, one can assume that alternative toll-free routes would be at least as congested during that hour. If these toll-free routes still remain congested (since they are not priced), could we expect some travelers from these alternative routes to shift to our priced bottleneck route to take advantage of the toll-free service in the 9 to 10am hour?

If you believe that some drivers will divert to the freeway, you will now see the paradox: Congestion Pricing Can Reduce Vehicular Travel Demand While At the Same Time Increasing Vehicle Throughput Through the Freeway Bottleneck

A paper describing other ways in which congestion pricing and active traffic management work together is available at:

Patrick DeCorla-Souza, AICP,
Federal Highway Administration,
Washington, DC,
Phone: 202-366-4076;

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